Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Curl and Convective Derivative

  1. Oct 5, 2015 #1
    Suppose u is a vector-valued function. Is it true that
    (∇×u)( (u⋅∇)u ) = (u⋅∇)(∇×u)⋅u

    ?

    Please note the lack of a dot product on the first two terms of the RHS and the parenthesis around the second term of the LHS. I'm trying to understand whether these differential operators are associative.
     
  2. jcsd
  3. Oct 6, 2015 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    There will be two ways of doing this. One is using existing vector calculus identities, if there are ones that would be helpful. In the absence of that, one has to fall back on plan B: write it out in full in terms of coordinates, using
    $$\nabla=\frac{\partial}{\partial x}+
    \frac{\partial}{\partial y}+
    \frac{\partial}{\partial z}$$

    $$\mathbf{a\cdot b}=\sum_{k=1}^3 a_kb_k$$
    and likewise the coordinate definition of curl.

    My guess is that it's correct, but the only way to be sure is to wade through the algebra.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Curl and Convective Derivative
  1. Divergence and Curl (Replies: 3)

  2. Inverse of the curl (Replies: 5)

  3. Curl Test (Replies: 3)

  4. Divergence of the Curl (Replies: 2)

  5. Definition of curl (Replies: 4)

Loading...